# Math Help - Explaining Similar Triangles

1. ## Explaining Similar Triangles

Hi
Is anybody able to put this in words for me?
(Why the pink and yellow triangles are similar)

Thanks

2. Hello, 200001

Is anybody able to put this in words for me?
(Why the two shaded triangles are similar.)
Code:
    A * - - - - - - - - - - - - - - - * F
|*  *                           |
|:*     *                       |
|::*        *                   |
| β *           *               |
|::::*              *           |
|:::::*                 *       |
|::::::* 9                  *   |
|:::::::*                       * E
|::::::::*                   *::|
|:::::::::*            3  *: α :|
|::::::::::*           *::::::::|
|:::::::::::*  90°  *:::::::::::|
|:::::::: α :*   *: β ::::::::::|
B * - - - - - - * - - - - - - - - * D
C

In right triangle $ABC$, let $\alpha \,=\,\angle ACB$

Then $\beta \,=\,\angle CAB$ is the complement of $\alpha\!:\;\;\beta \:=\:90^o - \alpha$

At point $C$, we have: . $\alpha + 90^o + \angle ECD \:=\:180^o \quad\Rightarrow\quad \angle ECD \:=\:90^o - \alpha$

. . Hence: . $\angle ECD \,=\,\beta$

In right triangle $CDE,\; \angle CED$ is the complement of $\angle ECD\:(\beta)$

. . Hence: . $\angle CED = \alpha$

Therefore: . $\Delta ABC \sim \Delta CDE\;\;(a.a.a)$

3. Awesome...thats perfect.
Thanks